it doesnt seem like ec. does the skin turn solid white when in contact with liquid? i assume not
dispute the fact that most people on this forum are strongly against dermotoligsts, the reason is only because they dont know how to treat ec. this is much more common and a reputable dermatologist may be able to help you, get your doctor to give you a referral and arrange to have a strip/patch test done to rule out contact dermatitis. However, i am in agreeance that you should think twice before accepting a strong chemical ointment your derm may prescribes, as this could make your situation worse, keep that as a last resort.
for the time being try leaving it alone, if peeling persists you may want to try a natural moisturizer such as lanolin
feel free to post a picture so people can get a better idea